• Journal of the Korea Society of Computer and Information
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• v.19 no.1
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• pp.57-64
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• 2014

As Steiner minimum tree building belongs to NP-Complete problem domain, heuristics for the problem ask for immense amount execution time and computations in numerous inputs. In this paper, we propose an efficient mechanism of euclidean Steiner minimum tree construction for numerous inputs using combination of Delaunay triangulation and Prim's minimum spanning tree algorithm. Trees built by proposed mechanism are compared respectively with the Prim's minimum spanning tree and minimums spanning tree based Steiner minimum tree. For 30,000 input nodes, Steiner minimum tree by proposed mechanism shows about 2.1% tree length less and 138.2% execution time more than minimum spanning tree, and does about 0.013% tree length less and 18.9% execution time less than minimum spanning tree based Steiner minimum tree in experimental results. Therefore the proposed mechanism can work moderately well to many useful applications where execution time is not critical but reduction of tree length is a key factor.

• The KIPS Transactions:PartA
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• v.14A no.5
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• pp.317-326
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• 2007

We propose more enhanced heuristic for the GOSST(Grade of Services Steiner Minimum Tree) problem in this paper. GOSST problem is a variation of Steiner Tree problem and to find a network topology satisfying the G-Condition with minimum network construction cost. GOSST problem is known as one of NP-Hard or NP-Complete problems. In previous our research, we proposed a heuristic employing Direct Steiner Point Locating strategy with Distance Preferring MST building strategy. In this paper, we propose new Steiner point locating strategy, Zigzag Steiner point Locating strategy. Through the results of out experiments, we can assert this strategy is better than our previous works. The Distance Zigzag GOSST method which hires the Distance Preferring MST building strategy and Zigzag Steiner point Locating strategy defrays the least network construction cost and brings 31.5% cost saving by comparison to G-MST, the experimental control and 2.2% enhancement by comparison to the Distance Direct GOSST method, the best GOSST method in our previous research.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.47 no.5
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• pp.25-34
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• 2010

By introducing additional nodes called Steiner points, the problem of Steiner Minimum Tree whose length can be shorter than Minimum Spanning Tree and which connects all input terminal nodes belongs to Non-Polynomial Complete domain. Though diverse heuristic methods can be applied to the problem, most of them may meet serious pains in computing and waiting for a solution of the problem with numerous input nodes. For numerous input nodes, an efficient PTAS approximation method producing candidate unit steiner trees with portals in most bottom layer, merging them hierarchically to construct their parent steiner trees in upper layer and building swiftly final approximation Steiner tree in most top layer is suggested in this paper. The experiment with 16,000 input nodes and designed 16 unit areas in most bottom layer shows 85.4% execution time improvement in serial processing and 98.9% in parallel processing comparing with pure Steiner heuristic method, though 0.24% overhead of tree length. Therefore, the suggested PTAS Steiner tree method can have a wide range applications to build a large scale approximation Steiner tree quickly.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.3
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• pp.191-197
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• 2011

The group Steiner tree problem is a generalization of the Steiner tree problem that is defined as follows. Given a weighted graph with a family of subsets of nodes, called groups, the problem is to find a minimum weighted tree that contains at least one node in each group. We present some existing and some new formulations for the problem and compare the relaxations of such formulations.

• Journal of the Korea Society of Computer and Information
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• v.17 no.7
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• pp.87-95
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• 2012

In this paper, PTAS three-dimensional Steiner minimum tree connecting numerous input nodes rapidly in 3D space is proposed. Steiner minimum tree problem belongs to NP problem domain, and when properly devised heuristic introduces, it is generally superior to other algorithms as minimum spanning tree affiliated with P problem domain. But when the number of input nodes is very large, the problem requires excessive execution time. In this paper, a method using PTAS is proposed to solve the difficulty. In experiments for 70,000 input nodes in 3D space, the tree produced by the proposed 8 space partitioned PTAS method reduced 86.88% execution time, compared with the tree by naive 3D steiner minimum tree method, though increased 0.81% tree length. This affirms the proposed method can work well for applications that many nodes of three dimensions are need to connect swifty, enduring slight increase of tree length.

• Journal of Korea Multimedia Society
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• v.11 no.1
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• pp.44-52
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• 2008

This paper is on the enhancement of our heuristics for Grade Of Services Steiner Minimum Tree (GOSST) problem that can apply to the design of communication networks offering manifold grade of services in multimedia communication area. GOSST problem known as one of NP-Hard problems asks for a network topology meeting the G-Condition with minimum construction cost. In our prior researches, we proposed some heuristics for the problem. In this paper, we suggest a strategy of G-Condition scrutiny sequence to fortify our previous heuristics. In the experiment results, the ameliorated achieves 71.9% economy of execution times, 28.9% of required Steiner points and 1.1% of network construction costs.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.430-434
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• 2008

The group Steiner tree problem is a generalization of the Steiner tree problem that is defined as follows. Given a weighted graph with a family of subsets of nodes, called groups, the problem is to find a minimum weighted tree that contains at least one node in each group. We present some existing and some new formulations for the problem and compare the relaxations of such formulations.

• Korean Management Science Review
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• v.23 no.1
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• pp.75-85
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• 2006

The rectilinear Steiner tree problem (RSTP) is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree(MST) on some set Steiner points. The RSTP is known to be NP-complete. The RSTP has received a lot of attention in the literature and heuristic and optimal algorithms have been proposed. A key performance measure of the algorithm for the RSTP is the reduction rate that is achieved by the difference between the objective value of the RSTP and that of the MST without Steiner points. A hybrid evolutionary strategy on RSTP based upon nodes set is presented. The computational results show that the hybrid evolutionary strategy is better than the previously proposed other heuristic. The average reduction rate of solutions from the evolutionary strategy is about 11.14%, which is almost similar to that of optimal solutions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.61
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• pp.33-39
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• 2000

In this paper, we present an algorithm for the multicast routing problem when there exit the cell replication limits of ATM switching nodes. This problem can be formulated as a Degree Constrained Minimum Steiner Tree Problem(DCSP). The proposed algorithm is a modification of the shortest path heuristic originally devised for minimum Steiner tree problem. From the experimental results, it can be seen that our algorithm is efficient to obtain a near optimal solution with comparatively low computational time.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.589-598
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• 2006

The rectilinear Steiner tree problem is to find a minimum-length rectilinear interconnection of a set of terminals in the plane. It is well known that the solution to this problem will be the minimal spanning tree (MST) on some set Steiner points. A hybrid evolutionary algorithm is introduced based upon the Prim algorithm. The Prim algorithm for the fitness evaluation requires heavy calculation time. The fitness value of parents is inherited to their child and the fitness value of child is estimated by the inherited structure of tree. We introduce four alternative evolutionary algorithms, Experiment result shows that the calculation time is reduced to 25% without loosing the solution quality by using the fitness estimation.